// \ingroup _graphbits

   //

   // \brief Extender for the BpGraphs

   template <typename Base>

   class BpGraphExtender : public Base {

     typedef Base Parent;

   public:

     typedef BpGraphExtender BpGraph;

     typedef True UndirectedTag;

     typedef typename Parent::Node Node;

     typedef typename Parent::Arc Arc;

     typedef typename Parent::Edge Edge;

     // BpGraph extension

     class RedNode : public Node {

     public:

       RedNode() {}

       RedNode(const RedNode& node) : Node(node) {}

       RedNode(Invalid) : Node(INVALID){}

       RedNode(const Node& node) : Node(node) {}

     };

     class BlueNode : public Node {

     public:

       BlueNode() {}

       BlueNode(const BlueNode& node) : Node(node) {}

       BlueNode(Invalid) : Node(INVALID){}

       BlueNode(const Node& node) : Node(node) {}

     };

     using Parent::first;

     using Parent::next;

     void first(RedNode& node) const {

       Parent::firstRed(node);

     }

     void next(RedNode& node) const {

       Parent::nextRed(node);

     }

     void first(BlueNode& node) const {

       Parent::firstBlue(node);

     }

     void next(BlueNode& node) const {

       Parent::nextBlue(node);

     }

     using Parent::id;

     int id(const RedNode& node) const {

       return Parent::redId(node);

     }

     int id(const BlueNode& node) const {

       return Parent::blueId(node);

     }

     int maxId(Node) const {

       return Parent::maxNodeId();

     }

     int maxId(RedNode) const {

       return Parent::maxRedId();

     }

     int maxId(BlueNode) const {

       return Parent::maxBlueId();

     }

     int maxId(Arc) const {

       return Parent::maxArcId();

     }

     int maxId(Edge) const {

       return Parent::maxEdgeId();

     }

     static Node fromId(int id, Node) {

       return Parent::nodeFromId(id);

     }

     static Arc fromId(int id, Arc) {

       return Parent::arcFromId(id);

     }

     static Edge fromId(int id, Edge) {

       return Parent::edgeFromId(id);

     }

     Node oppositeNode(const Node &n, const Edge &e) const {

       if( n == Parent::u(e))

         return Parent::v(e);

       else if( n == Parent::v(e))

         return Parent::u(e);

       else

         return INVALID;

     }

     Arc oppositeArc(const Arc &arc) const {

       return Parent::direct(arc, !Parent::direction(arc));

     }

     using Parent::direct;

     Arc direct(const Edge &edge, const Node &node) const {

       return Parent::direct(edge, Parent::u(edge) == node);

     }

     // Alterable extension

     typedef AlterationNotifier<BpGraphExtender, Node> NodeNotifier;

     typedef AlterationNotifier<BpGraphExtender, RedNode> RedNodeNotifier; 

     typedef AlterationNotifier<BpGraphExtender, BlueNode> BlueNodeNotifier;

     typedef AlterationNotifier<BpGraphExtender, Arc> ArcNotifier;

     typedef AlterationNotifier<BpGraphExtender, Edge> EdgeNotifier;

   protected:

     mutable NodeNotifier node_notifier;

     mutable RedNodeNotifier red_node_notifier;

     mutable BlueNodeNotifier blue_node_notifier;

     mutable ArcNotifier arc_notifier;

     mutable EdgeNotifier edge_notifier;

   public:

     NodeNotifier& notifier(Node) const {

       return node_notifier;

     }

     RedNodeNotifier& notifier(RedNode) const {

       return red_node_notifier;

     }

     BlueNodeNotifier& notifier(BlueNode) const {

       return blue_node_notifier;

     }

     ArcNotifier& notifier(Arc) const {

       return arc_notifier;

     }

     EdgeNotifier& notifier(Edge) const {

       return edge_notifier;

     }

     class NodeIt : public Node {

       const BpGraph* _graph;

     public:

       NodeIt() {}

       NodeIt(Invalid i) : Node(i) { }

       explicit NodeIt(const BpGraph& graph) : _graph(&graph) {

         _graph->first(static_cast<Node&>(*this));

       }

       NodeIt(const BpGraph& graph, const Node& node)

         : Node(node), _graph(&graph) {}

       NodeIt& operator++() {

         _graph->next(*this);

         return *this;

       }

     };

     class RedIt : public Node {

       const BpGraph* _graph;

     public:

       RedIt() {}

       RedIt(Invalid i) : Node(i) { }

       explicit RedIt(const BpGraph& graph) : _graph(&graph) {

         _graph->firstRed(static_cast<Node&>(*this));

       }

       RedIt(const BpGraph& graph, const Node& node)

         : Node(node), _graph(&graph) {

         LEMON_DEBUG(_graph->red(node), "Node has to be red.");

       }

       RedIt& operator++() {

         _graph->nextRed(*this);

         return *this;

       }

     };

     class BlueIt : public Node {

       const BpGraph* _graph;

     public:

       BlueIt() {}

       BlueIt(Invalid i) : Node(i) { }

       explicit BlueIt(const BpGraph& graph) : _graph(&graph) {

         _graph->firstBlue(static_cast<Node&>(*this));

       }

       BlueIt(const BpGraph& graph, const Node& node)

         : Node(node), _graph(&graph) {

         LEMON_DEBUG(_graph->blue(node), "Node has to be blue.");

       }

       BlueIt& operator++() {

         _graph->nextBlue(*this);

         return *this;

       }

     };

     class ArcIt : public Arc {

       const BpGraph* _graph;

     public:

       ArcIt() { }

       ArcIt(Invalid i) : Arc(i) { }

       explicit ArcIt(const BpGraph& graph) : _graph(&graph) {

         _graph->first(static_cast<Arc&>(*this));

       }

       ArcIt(const BpGraph& graph, const Arc& arc) :

         Arc(arc), _graph(&graph) { }

       ArcIt& operator++() {

         _graph->next(*this);

         return *this;

       }

     };

     class OutArcIt : public Arc {

       const BpGraph* _graph;

     public:

       OutArcIt() { }

       OutArcIt(Invalid i) : Arc(i) { }

       OutArcIt(const BpGraph& graph, const Node& node)

         : _graph(&graph) {

         _graph->firstOut(*this, node);

       }

       OutArcIt(const BpGraph& graph, const Arc& arc)

         : Arc(arc), _graph(&graph) {}

       OutArcIt& operator++() {

         _graph->nextOut(*this);

         return *this;

       }

     };

     class InArcIt : public Arc {

       const BpGraph* _graph;

     public:

       InArcIt() { }

       InArcIt(Invalid i) : Arc(i) { }

       InArcIt(const BpGraph& graph, const Node& node)

         : _graph(&graph) {

         _graph->firstIn(*this, node);

       }

       InArcIt(const BpGraph& graph, const Arc& arc) :

         Arc(arc), _graph(&graph) {}

       InArcIt& operator++() {

         _graph->nextIn(*this);

         return *this;

       }

     };

     class EdgeIt : public Parent::Edge {

       const BpGraph* _graph;

     public:

       EdgeIt() { }

       EdgeIt(Invalid i) : Edge(i) { }

       explicit EdgeIt(const BpGraph& graph) : _graph(&graph) {

         _graph->first(static_cast<Edge&>(*this));

       }

       EdgeIt(const BpGraph& graph, const Edge& edge) :

         Edge(edge), _graph(&graph) { }

       EdgeIt& operator++() {

         _graph->next(*this);

         return *this;

       }

     };

     class IncEdgeIt : public Parent::Edge {

       friend class BpGraphExtender;

       const BpGraph* _graph;

       bool _direction;

     public:

       IncEdgeIt() { }

       IncEdgeIt(Invalid i) : Edge(i), _direction(false) { }

       IncEdgeIt(const BpGraph& graph, const Node &node) : _graph(&graph) {

         _graph->firstInc(*this, _direction, node);

       }

       IncEdgeIt(const BpGraph& graph, const Edge &edge, const Node &node)

         : _graph(&graph), Edge(edge) {

         _direction = (_graph->source(edge) == node);

       }

       IncEdgeIt& operator++() {

         _graph->nextInc(*this, _direction);

         return *this;

       }

     };

     // \brief Base node of the iterator

     //

     // Returns the base node (ie. the source in this case) of the iterator

     Node baseNode(const OutArcIt &arc) const {

       return Parent::source(static_cast<const Arc&>(arc));

     }

     // \brief Running node of the iterator

     //

     // Returns the running node (ie. the target in this case) of the

     // iterator

     Node runningNode(const OutArcIt &arc) const {

       return Parent::target(static_cast<const Arc&>(arc));

     }

     // \brief Base node of the iterator

     //

     // Returns the base node (ie. the target in this case) of the iterator

     Node baseNode(const InArcIt &arc) const {

       return Parent::target(static_cast<const Arc&>(arc));

     }

     // \brief Running node of the iterator

     //

     // Returns the running node (ie. the source in this case) of the

     // iterator

     Node runningNode(const InArcIt &arc) const {

       return Parent::source(static_cast<const Arc&>(arc));

     }

     // Base node of the iterator

     //

     // Returns the base node of the iterator

     Node baseNode(const IncEdgeIt &edge) const {

       return edge._direction ? this->u(edge) : this->v(edge);

     }

     // Running node of the iterator

     //

     // Returns the running node of the iterator

     Node runningNode(const IncEdgeIt &edge) const {

       return edge._direction ? this->v(edge) : this->u(edge);

     }

     // Mappable extension

     template <typename _Value>

     class NodeMap

       : public MapExtender<DefaultMap<BpGraph, Node, _Value> > {

       typedef MapExtender<DefaultMap<BpGraph, Node, _Value> > Parent;

     public:

       explicit NodeMap(const BpGraph& bpgraph)

         : Parent(bpgraph) {}

       NodeMap(const BpGraph& bpgraph, const _Value& value)

         : Parent(bpgraph, value) {}

     private:

       NodeMap& operator=(const NodeMap& cmap) {

         return operator=<NodeMap>(cmap);

       }

       template <typename CMap>

       NodeMap& operator=(const CMap& cmap) {

         Parent::operator=(cmap);

         return *this;

       }

     };

     template <typename _Value>

     class RedMap

       : public MapExtender<DefaultMap<BpGraph, RedNode, _Value> > {

       typedef MapExtender<DefaultMap<BpGraph, RedNode, _Value> > Parent;

     public:

       explicit RedMap(const BpGraph& bpgraph)

         : Parent(bpgraph) {}

       RedMap(const BpGraph& bpgraph, const _Value& value)

         : Parent(bpgraph, value) {}

     private:

       RedMap& operator=(const RedMap& cmap) {

         return operator=<RedMap>(cmap);

       }

       template <typename CMap>

       RedMap& operator=(const CMap& cmap) {

         Parent::operator=(cmap);

         return *this;

       }

     };

     template <typename _Value>

     class BlueMap

       : public MapExtender<DefaultMap<BpGraph, BlueNode, _Value> > {

       typedef MapExtender<DefaultMap<BpGraph, BlueNode, _Value> > Parent;

     public:

       explicit BlueMap(const BpGraph& bpgraph)

         : Parent(bpgraph) {}

       BlueMap(const BpGraph& bpgraph, const _Value& value)

         : Parent(bpgraph, value) {}

     private:

       BlueMap& operator=(const BlueMap& cmap) {

         return operator=<BlueMap>(cmap);

       }

       template <typename CMap>

       BlueMap& operator=(const CMap& cmap) {

         Parent::operator=(cmap);

         return *this;

       }

     };

     template <typename _Value>

     class ArcMap

       : public MapExtender<DefaultMap<BpGraph, Arc, _Value> > {

       typedef MapExtender<DefaultMap<BpGraph, Arc, _Value> > Parent;

     public:

       explicit ArcMap(const BpGraph& graph)

         : Parent(graph) {}

       ArcMap(const BpGraph& graph, const _Value& value)

         : Parent(graph, value) {}

     private:

       ArcMap& operator=(const ArcMap& cmap) {

         return operator=<ArcMap>(cmap);

       }

       template <typename CMap>

       ArcMap& operator=(const CMap& cmap) {

         Parent::operator=(cmap);

         return *this;

       }

     };

     template <typename _Value>

     class EdgeMap

       : public MapExtender<DefaultMap<BpGraph, Edge, _Value> > {

       typedef MapExtender<DefaultMap<BpGraph, Edge, _Value> > Parent;

     public:

       explicit EdgeMap(const BpGraph& graph)

         : Parent(graph) {}

       EdgeMap(const BpGraph& graph, const _Value& value)

         : Parent(graph, value) {}

     private:

       EdgeMap& operator=(const EdgeMap& cmap) {

         return operator=<EdgeMap>(cmap);

       }

       template <typename CMap>

       EdgeMap& operator=(const CMap& cmap) {

         Parent::operator=(cmap);

         return *this;

       }

     };

     // Alteration extension

     Node addRedNode() {

       Node node = Parent::addRedNode();

       notifier(RedNode()).add(node);

       notifier(Node()).add(node);

       return node;

     }

     Node addBlueNode() {

       Node node = Parent::addBlueNode();

       notifier(BlueNode()).add(node);

       notifier(Node()).add(node);

       return node;

     }

     Edge addEdge(const Node& from, const Node& to) {

       Edge edge = Parent::addEdge(from, to);

       notifier(Edge()).add(edge);

       std::vector<Arc> av;

       av.push_back(Parent::direct(edge, true));

       av.push_back(Parent::direct(edge, false));

       notifier(Arc()).add(av);

       return edge;

     }

     void clear() {

       notifier(Arc()).clear();

       notifier(Edge()).clear();

       notifier(Node()).clear();

       notifier(BlueNode()).clear();

       notifier(RedNode()).clear();

       Parent::clear();

     }

     template <typename BpGraph, typename NodeRefMap, typename EdgeRefMap>

     void build(const BpGraph& graph, NodeRefMap& nodeRef,

                EdgeRefMap& edgeRef) {

       Parent::build(graph, nodeRef, edgeRef);

       notifier(RedNode()).build();

       notifier(BlueNode()).build();

       notifier(Node()).build();

       notifier(Edge()).build();

       notifier(Arc()).build();

     }

     void erase(const Node& node) {

       Arc arc;

       Parent::firstOut(arc, node);

       while (arc != INVALID ) {

         erase(arc);

         Parent::firstOut(arc, node);

       }

       Parent::firstIn(arc, node);

       while (arc != INVALID ) {

         erase(arc);

         Parent::firstIn(arc, node);

       }

       if (Parent::red(node)) {

         notifier(RedNode()).erase(node);

       } else {

         notifier(BlueNode()).erase(node);        

       }

       notifier(Node()).erase(node);

       Parent::erase(node);

     }

     void erase(const Edge& edge) {

       std::vector<Arc> av;

       av.push_back(Parent::direct(edge, true));

       av.push_back(Parent::direct(edge, false));

       notifier(Arc()).erase(av);

       notifier(Edge()).erase(edge);

       Parent::erase(edge);

     }

     BpGraphExtender() {

       red_node_notifier.setContainer(*this);

       blue_node_notifier.setContainer(*this);

       node_notifier.setContainer(*this);

       arc_notifier.setContainer(*this);

       edge_notifier.setContainer(*this);

     }

     ~BpGraphExtender() {

       edge_notifier.clear();

       arc_notifier.clear();

       node_notifier.clear();

       blue_node_notifier.clear();

       red_node_notifier.clear();

     }

   };